Question

If A=x^2 and dx/dt=3, find dA/dt|x= 10

how do i do this

because it also says to find dx/dt|x=10 and dA/dt=3

Answer 1

lol no

Answer 2

\[A=x^2, A'=2xx'\]

Answer 3

you are told \(x'=3\) and \(x=10\) so
\[A'=2\times 10\times 3=60\]

Answer 4

since the dx/dt notation sucks,i replaced it by \(x'\) which is easier to write

Answer 5

hope the answer was clear

Answer 6

If A=x^2 and dx/dt=3, find dA/dt|x= 10
dA/dx = 2 x
dA/dx*dx/dt = dA/dt

substitute
2 x * 3 = 10
x = 10/6 = 5/3

Answer 7

what is the original question?

Answer 8

A=x^2 is the equation then it says to do the two things

Answer 9

are you to find dA/dt when x = 10 given that dx/dt = 3 and dA/dt when x = 3

Answer 10

are those the 2 things?

Answer 11

yes two separate

Answer 12

yes that makes sense now

Answer 13

dA/dx*dx/dt = dA/dt
x = 10 and dx/dt = 3
dA/dx = 2 x = 2 * 10 = 20
substituting
dA/dt = 20*3 = 60

Answer 14

but i dont get what the diference si between dx/dt and dA/dt

Answer 15

dA/dt when x = 3

Answer 16

dx/dt function x changing with t
da/dt change in area with respect to t

Answer 17

dx/dt = 3 and x = 3
da/dt = da/dx*dx/dt = 2 * 3 * 3 = 18